Is this sentence gramatically correct Cut the cheese thin?

The sentence "Cut the cheese thin" is grammatically correct, but it's a bit informal. A more formal way to say it would be:

* Cut the cheese thinly.

"Thinly" is an adverb, which modifies the verb "cut" and specifies how the cheese should be cut.

Here's another way to phrase it:

* Slice the cheese thinly.

This emphasizes the slicing action.